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* @license Apache-2.0
*
* Copyright (c) 2025 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MAIN //
/**
* Computes the variance of a strided array using a one-pass textbook algorithm.
*
* @private
* @param {PositiveInteger} N - number of indexed elements
* @param {number} correction - degrees of freedom adjustment
* @param {Object} x - input array object
* @param {Collection} x.data - input array data
* @param {Array<Function>} x.accessors - array element accessors
* @param {integer} strideX - stride length
* @param {NonNegativeInteger} offsetX - starting index
* @returns {number} variance
*
* @example
* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
*
* var x = toAccessorArray( [ 1.0, -2.0, 2.0 ] );
*
* var v = variancetk( x.length, 1, arraylike2object( x ), 1, 0 );
* // returns ~4.3333
*/
function variancetk( N, correction, x, strideX, offsetX ) {
var xbuf;
var get;
var S2;
var ix;
var S;
var v;
var n;
var i;
n = N - correction;
if ( N <= 0 || n <= 0.0 ) {
return NaN;
}
// Cache reference to array data:
xbuf = x.data;
// Cache a reference to the element accessor:
get = x.accessors[ 0 ];
if ( N === 1 || strideX === 0 ) {
return get( xbuf, offsetX );
}
ix = offsetX;
S2 = 0.0;
S = 0.0;
for ( i = 0; i < N; i++ ) {
v = get( xbuf, ix );
S2 += v * v;
S += v;
ix += strideX;
}
return (S2 - ((S/N)*S)) / n;
}
// EXPORTS //
module.exports = variancetk;
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